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MATH0200 online PLACEMENT TEST 182 QUESTIONS 11-08-13 Fall 2013
elementary and intermediate AlgebraWarm-up
Name___________________________________atfm0303mk2810yes
website www.alvarezmathhelp.comPROGRAMS ALVAREZLAB (SAVE AND EXTRACT TO YOUR COMPUTER)
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INTERACTMATH (MCKENNA AND KIRK BEGINNING AND INTERMEDIATE ALG)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Subtract.
1) 40 - (-54)
A) -14 B) 94 C) 14 D) -94
1)
Objective: (1.3) Subtract Real Numbers
2) (-8) - (-22)
A) -14 B) 30 C) 14 D) -30
2)
Objective: (1.3) Subtract Real Numbers
Perform the indicated operations.
3) 17 - (-19) + 14 + (-18)
A) 32 B) -4 C) 30 D) -30
3)
Objective: (1.3) Add/Subtract More Than Two Real Numbers
Evaluate.
4) -102
A) -20 B) -1000 C) -100 D) -1024
4)
Objective: (1.5) Evaluate Exponential Expression
5) (-6)2
A) -36 B) -12 C) 12 D) 36
5)
Objective: (1.5) Evaluate Exponential Expression
Simplify using the order of operations.
6) 8 + 2(-4 - 1)
A) 2 B) 14 C) -2 D) -1
6)
Objective: (1.5) Simplify Using Order of Operations
Evaluate the following algebraic expression using the indicated values.
7)8(a - b)
-9c - d when a = 7, b = 0, c = -9, d = 82
A) 28 B) -56 C) - 28 D) 56
7)
Objective: (1.5) Evaluate Algebraic Expression Using Indicated Values
Simplify by combining like terms.
8) -9x - 3x
A) -12x B) -12 + x C) -6x D) 27x
8)
Objective: (1.5) Simplify by Combining Like Terms
1
9) 7a - 2a + 5b
A) -5a + 5b B) 9a + 5b C) 10a D) 5a + 5b
9)
Objective: (1.5) Simplify by Combining Like Terms
10) 7x + 6 + 3x - x + 4
A) 11x + 10 B) 9x + 10 C) 10x + 10 D) 10x - 10
10)
Objective: (1.5) Simplify by Combining Like Terms
11) 3x2 - 9x - 4 + 5x - 6 + 9x2
A) 5x2 + 8x - 15 B) 12x2 - 4x - 10 C) -2x3 D) 12x4 - 4x2 - 10
11)
Objective: (1.5) Simplify by Combining Like Terms
Use the Distributive Property to remove parentheses, and then combine like terms.
12) 9(y + 8) - 6
A) 9y + 18 B) 9y + 2 C) 9y + 66 D) 17y - 6
12)
Objective: (1.5) Use Distributive Property and Combine Like Terms
13) 9x - (7 - 3x)
A) 6x - 7 B) 12x + 7 C) 12x - 7 D) 9x - 10
13)
Objective: (1.5) Use Distributive Property and Combine Like Terms
14) 4x + 8 - 2(-4x - 8)
A) -8x - 16 B) -12x - 24 C) 12x + 24 D) 8x + 16
14)
Objective: (1.5) Use Distributive Property and Combine Like Terms
15) -4(9r + 7) + 6(3r + 5)
A) -18r + 2 B) -18r + 7 C) 5r + 3 D) -64r
15)
Objective: (1.5) Use Distributive Property and Combine Like Terms
Solve the linear equation and check the solution.
16) 13(x - 52) = 26
A) {52} B) {26} C) {50} D) {54}
16)
Objective: (2.2) Solve Linear Equation (Grouping Symbols)
17) 6x - (5x - 1) = 2
A) 1 B) - 1
11C) - 1 D)
1
11
17)
Objective: (2.2) Solve Linear Equation (Grouping Symbols)
18) -7x + 3(2x - 4) = -9 - 4x
A)21
5B) {1} C) {- 1} D) - 7
18)
Objective: (2.2) Solve Linear Equation (Grouping Symbols)
19) -7q + 1.0 = -24.5 - 1.9q
A) {5} B) {3.9} C) {-31} D) {3.6}
19)
Objective: (2.2) Solve Linear Equation (Decimals)
2
20)1
2x +
6
5 =
2
5x
A) {-16} B) {16} C) {12} D) {-12}
20)
Objective: (2.2) Solve Linear Equation (Fractions)
21)7
3 -
x
3 =
x
4
A) {7} B) {4} C) {-4} D)28
5
21)
Objective: (2.2) Solve Linear Equation (Fractions)
22)r + 6
5 =
r + 8
7
A) {1} B) {2} C) {-2} D) {-1}
22)
Objective: (2.2) Solve Linear Equation (Fractions)
23)17x
16 +
x
16 = 6x +
1
8 +
15
16x
A) - 2
93B)
1
93C) -
1
93D)
2
99
23)
Objective: (2.2) Solve Linear Equation (Fractions)
Solve for the indicated variable.
24) A = P(1 + rt), for t
A) t = Pr
A - PB) t =
A
rC) t =
P - A
PrD) t =
A - P
Pr
24)
Objective: (2.3) Solve Literal Equation for Variable
25) A = 1
2h(a + b), for a
A) a = A - hb
2hB) a =
hb - 2A
hC) a =
2Ab - h
hD) a =
2A - hb
h
25)
Objective: (2.3) Solve Literal Equation for Variable
3
Solve the problem by utilizing the 4Pʹs: Prepare, Plan, Process, and Ponder.
26) Solve the formula for the volume of a right circular cone, V = 1
3πr2h, for the height (h). Determine
the height of a right circular cone with a radius of 2 meters and a volume of 16π cubic meters.
A) h = 3V
πr2; h = 24 m B) h =
3V
πr2; h = 12 m
C) h = 3V
πr2; h = 8 m D) h =
3V
πr2; h = 4 m
26)
Objective: (2.3) Solve 4Ps Application
Solve for the indicated variable.
27) -16 = -9p + 3q, for p
A) p = 9 - 16q
3B) p =
16 + 3q
9C) p = -16 - 3q D) p =
16 - 3q
-9
27)
Objective: (2.3) Solve Challenge Problems
28)x
a +
y
b = 1, for x
A) x = a 1- y
bB) x = a
y
b - 1 C) x = b 1-
y
aD) x = a 1+
y
b
28)
Objective: (2.3) Solve Challenge Problems
29) ax + by = c, for x
A) x = c - ay
bB) x =
c + ay
bC) x =
c - by
aD) x =
c + by
a
29)
Objective: (2.3) Solve Challenge Problems
4
Solve the linear inequality and graph the solution set. State the solution using interval notation.
30) 4x - 4 ≥ 20
A) [4, ∞)
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
B) [6, ∞)
-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
C) (-∞, 4]
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
D) (-∞, 6]
-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13
30)
Objective: (2.4) Solve and Graph Linear Inequality
31) 36 - 6x ≥ -6
A) (-∞, -5]
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
B) [-5, ∞)
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
C) [7, ∞)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 140 1 2 3 4 5 6 7 8 9 10 11 12 13 14
D) (-∞, 7]
0 1 2 3 4 5 6 7 8 9 10 11 12 13 140 1 2 3 4 5 6 7 8 9 10 11 12 13 14
31)
Objective: (2.4) Solve and Graph Linear Inequality
Solve the linear inequality and state the solution set using interval notation, if applicable.
32)x
2 ≥ 3 +
x
8
A) [8, ∞) B) [-8, ∞) C) (8, ∞) D) (-∞, 8]
32)
Objective: (2.4) Solve Linear Inequality
5
Solve the inequality for x. Write the answer using interval notation.
33)x + 7
6 -
5
48 >
x + 3
8
A) - 33
2, ∞ B) -∞, -
33
2C) -∞, -
43
14D)
79
2, ∞
33)
Objective: (2.4) Solve Challenge Problems
Solve the double inequality for x. State the solution using interval notation.
34) 13 ≤ 3x + 1 ≤ 19
A) [4, 6] B) [-6, -4] C) (4, 6) D) (-6, -4)
34)
Objective: (2.5) Solve Double Inequality
Solve the absolute value equation and write the solution set using set notation.
35) |r - 2| = 5
A) {-7} B) {-3, 7} C) { } D) {3, 7}
35)
Objective: (2.6) Solve Absolute Value Equations
Solve the absolute value inequality. Graph the solution set, then write the answer using interval notation.
36) |x - 9| < 16
A) (-∞, 25)
5 10 15 20 25 30 35 40 455 10 15 20 25 30 35 40 45
B) (-25, 7)
-25 -20 -15 -10 -5 0 5 10 15-25 -20 -15 -10 -5 0 5 10 15
C) (-7, 25)
-5 0 5 10 15 20 25 30 35-5 0 5 10 15 20 25 30 35
D) (-∞, -7)
-25 -20 -15 -10 -5 0 5 10-25 -20 -15 -10 -5 0 5 10
36)
Objective: (2.6) Solve and Graph Absolute Value Inequality (<, ≤)
6
Solve the absolute value equation or inequality. State the solution using set notation or interval notation, whichever is
appropriate.
37) |x + 6| > 16
A) (-10, 22)
-10 -5 0 5 10 15 20 25 30-10 -5 0 5 10 15 20 25 30
B) (10, ∞)
-20 -15 -10 -5 0 5 10 15 20-20 -15 -10 -5 0 5 10 15 20
C) (-∞, -22) ∪ (10, ∞)
-20 -15 -10 -5 0 5 10 15 20-20 -15 -10 -5 0 5 10 15 20
D) (-22, 10)
-20 -15 -10 -5 0 5 10 15 20-20 -15 -10 -5 0 5 10 15 20
37)
Objective: (2.6) Solve and Graph Absolute Value Inequality (>, ≥)
Determine if the ordered pair is a solution to the equation.
38) (3, 5) 5x + y = 20
A) yes B) no
38)
Objective: (3.1) Determine if Ordered Pair Is Solution to Equation
Use the intercept method to graph the solutions of the linear equation.
39) 2x - 3y = 6
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
A)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
B)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
39)
7
C)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
D)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
Objective: (3.2) Graph Linear Equation Using Intercept Method
Find the slope of the straight line through the two solution points.
40) (8, 3) and (-4, 4)
A) m = - 5
8B) m = - 12 C) m = -
1
12D) m = -
8
5
40)
Objective: (3.3) Find Slope of Line Given Two Points
Find the slope and the y-intercept by using the slope-intercept form of the equation of the line. If necessary, solve for y
first.
41) 2x - 3y = -8
A) m = 3
2, 0, - 4 B) m =
2
3, 0,
8
3
C) m = - 2
3, 0,
8
3D) m = -
2
3, 0, -
8
3
41)
Objective: (3.3) Find Slope and y-Intercept Given Equation
Graph the solutions of the linear equation by using the slope and y -intercept.
42) y = 2x - 6
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
42)
8
A)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
B)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
C)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
D)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
Objective: (3.3) Graph Linear Equation Using Slope and y-Intercept
Write the equation of the line having the given slope and passing through the given point.
43) m = 3, (-3, 6)
A) x = 3y - 15 B) y = 3x - 15 C) x = 3y + 15 D) y = 3x + 15
43)
Objective: (3.4) Write Equation of Line Given Slope and Point
Determine if the pair of lines is parallel, perpendicular, or neither.
44) y = 6x - 8
y = - 1
6x - 1
A) parallel B) perpendicular C) neither
44)
Objective: (3.4) Determine if Lines Are Parallel, Perpendicular, or Neither
45) y = 9x - 6
y = 9x + 4
A) perpendicular B) parallel C) neither
45)
Objective: (3.4) Determine if Lines Are Parallel, Perpendicular, or Neither
46) y = 5x - 4
y = -5x - 8
A) parallel B) perpendicular C) neither
46)
Objective: (3.4) Determine if Lines Are Parallel, Perpendicular, or Neither
9
Solve the system of linear equations using the Substitution Method.
47) x + y = 10
3x + 5y = 16
A) {(17, -7)} B) {(x, y) x + y = 10}
C) { } D) {(3, 7)}
47)
Objective: (4.2) Solve System of Linear Equations Using Substitution
48) x + y = 16
y = 3x
A) { } B) {(-4, -12)}
C) {(4, 12)} D) {(x, y) x + y = 16}
48)
Objective: (4.2) Solve System of Linear Equations Using Substitution
49) 8x - 4y = 8
2x - y = 5
A) {(4, -3)} B) {(x, y) 8x - 4y = 8}
C) {(-4, 13)} D) { }
49)
Objective: (4.2) Solve System of Linear Equations Using Substitution (Inconsistent/Dependent)
Solve the system of linear equations using the Elimination Method.
50) x - y = 7
x + y = 5
A) { } B) {(-6, -13)}
C) {(x, y) x - y = 7} D) {(6, -1)}
50)
Objective: (4.3) Solve System of Linear Equations Using Elimination
51) 0.03x - 0.1y = 1
-0.2x + 0.02y = 58
A) {(300, 80)} B) {(-300, -100)}
C) {(x, y) 0.03x - 0.1y = 1} D) { }
51)
Objective: (4.3) Solve Challenge Problem
Subtract. Write the difference in descending powers of the variable.
52) (8x2 - 5x + 20) - (3x2 + 5x - 40)
A) 5x2 + 10x - 60 B) 5x2 - 10x - 20 C) 5x2 + 10x + 60 D) 5x2 - 10x + 60
52)
Objective: (5.3) Subtract Polynomials
Evaluate the polynomial with the indicated value for the variable.
53) -2x3 - 5x2 - x - 46 for x = -2
A) -58 B) -18 C) -48 D) -60
53)
Objective: (5.3) Evaluate Polynomial
Multiply the monomials.
54) (-4x3y4)(-5x2y2)
A) 20x6y5 B) 20x5y6 C) 20xy6 D) 20xy5
54)
Objective: (5.4) Multiply Monomial by Monomial
10
Multiply.
55) 9x(-10x - 2)
A) -10x2 - 18x B) -108x2 C) -90x2 - 2x D) -90x2 - 18x
55)
Objective: (5.4) Mulitply Monomial by Polynomial
Multiply using the Distributive Property.
56) (y + 4)(y + 7)
A) 2y2 + 28 B) 2y + 28 C) y2 + 11y + 11 D) y2 + 11y + 28
56)
Objective: (5.4) Multiply Binomial by Binomial
57) (2x - 10)(x - 12)
A) x2 + 120x - 34 B) 2x2 + 31x + 120 C) 2x2 - 34x + 120 D) x2 - 34x + 31
57)
Objective: (5.4) Multiply Binomial by Binomial
58) (5x + 7)(4x - 10)
A) 20x2 - 22x - 22 B) 9x2 - 22x - 22 C) 20x2 - 22x - 70 D) 9x2 - 22x - 70
58)
Objective: (5.4) Multiply Binomial by Binomial
59) (x - 11y)(5x + 6y)
A) 5x2 - 49xy - 66y2 B) 5x2 - 49xy - 49y2
C) x2 - 49xy - 49y2 D) x2 - 49xy - 66y2
59)
Objective: (5.4) Multiply Binomial by Binomial
Multiply.
60) (x + 1)(x2 - x + 1)
A) x3 - 2x2 - 2x - 1 B) x3 + 1
C) x3 + 2x2 + 2x + 1 D) x3 - 1
60)
Objective: (5.4) Multiply Polynomial by Polynomial
11
Solve the problem by utilizing the 4Pʹs: Prepare, Plan, Process, and Ponder.
61) Use the figure to:
a. Find the exact area of the shaded region leaving π in the answer.
b. Find the approximate area (in square yards) by letting x = 5 yards and π ≈ 3.14
1
4x
2x + 4
2x + 4
A) a. - (64 + π)
16x2 - 16x - 16 units2
b. -191.09 yd2
B) a. (64 - π)
16x2 + 16x + 16 units2
b. 191.09 yd2
C) a. (64 + π)
16x2 + 16x + 16 units2
b. 200.91 yd2
D) a. (4 - π)
16x2 + 16x + 16 units2
b. 97.34 yd2
61)
Objective: (5.4) Solve 4Ps Application
12
62) Use the figures to:
a. Find the areas of the two triangles and write the answers as polynomials. Recall that the area of
a triangle is given by A = 1
2bh.
b. If x = 8 meters, find the numeric values for each area in square meters.
4x x + 8
5x2 - 4x + 3 x2 - 3x + 8
A) a. 20x3 - 16x2 + 12x units2; x3 + 5x2 - 16x + 64 units2
b. 9312m2; 768 m2
B) a. 10x3 - 8x2 - 6x units2; 1
2x3 +
5
2x2 - 8x - 32 units2
b. 4560 m2; 640 m2
C) a. 10x3 + 8x2 + 6x units2; 1
2x3 +
5
2x2 + 8x + 32 units2
b. 5680 m2; 512m2
D) a. 10x3 - 8x2 + 6x units2; 1
2x3 +
5
2x2 - 8x + 32 units2
b. 4656 m2; 384 m2
62)
Objective: (5.4) Solve 4Ps Application
Multiply using the FOIL method.
63) (a + 5)(a + 5)
A) a2 + 10a + 10 B) 2a + 25 C) 2a2 + 25 D) a2 + 10a + 25
63)
Objective: (5.5) Multiply Two Binomials Using FOIL Method
64) (m - a )2
A) m2 + 2ma + a2 B) m2 - 2ma + a2 C) m2 - ma + a2 D) m2 - 2ma - a2
64)
Objective: (5.5) Multiply Two Binomials Using FOIL Method
Square using special products.
65) (x + 3 )2
A) x2 + 6 x + 9 B) 9 x2 + 6 x + 9 C) x2 + 9 D) x + 9
65)
Objective: (5.5) Square Binomial
66) (9 a - 11 )2
A) 9 a2 + 121 B) 81 a2 + 121
C) 81 a2 - 198 a + 121 D) 9 a2 - 198 a + 121
66)
Objective: (5.5) Square Binomial
13
67) (4 b + 5 )2
A) 16b2 + 40b + 25 B) 4 b2 + 40b + 25
C) 4 b2 + 25 D) 16b2 + 25
67)
Objective: (5.5) Square Binomial
68) (4 x - 11y)2
A) 16x2 - 88xy + 121 y2 B) 4 x2 - 88xy + 121 y2
C) 4 x2 + 121 y2 D) 16x2 + 121 y2
68)
Objective: (5.5) Square Binomial
Use the special product of a sum and difference of two terms to multiply the binomials.
69) (x + 5 )(x - 5 )
A) x2 + 10x - 25 B) x2 - 25 C) x2 - 10 D) x2 - 10x - 25
69)
Objective: (5.5) Multiply Sum and Difference of Two Terms
70) (x + 8y)(x - 8y)
A) x2 - 16y2 B) x2 - 64y2
C) x2 - 16xy - 64y2 D) x2 + 16xy - 64y2
70)
Objective: (5.5) Multiply Sum and Difference of Two Terms
71) (10 a + 3 b)( 10 a - 3 b)
A) 100 a2 - 60ab - 9 b2 B) 10 a2 - 3 b2
C) 100 a2 + 60ab - 9 b2 D) 100 a2 - 9 b2
71)
Objective: (5.5) Multiply Sum and Difference of Two Terms
Find the area of the geometric figure using special products.
72)
3x + 3
3x + 3
A) 9x2 + 9 B) 6x2 + 18x + 6 C) 9x2 + 9x + 9 D) 9x2 + 18x + 9
72)
Objective: (5.5) Solve Application
14
73)
6x - 1
6x - 1
A) 18x2 - 6x + 1
2B) 36x2 - 12x - 1 C) 18x2 + 6x -
1
2D) 36x2 - 12x + 1
73)
Objective: (5.5) Solve Application
Divide. Write answer in lowest terms using positive powers only.
74)-42x9y13z6
7x6y8z5
A) -6x2y4z B) x3y5z C) -6x3y5z D) -6x3y5
74)
Objective: (5.6) Divide Using Exponent Rules
Divide. Do not use long division.
75)12a3 - 9a5 + 15a
3a
A) 4a2 - 3a4 - 5 B) 4a2 - 9a5 + 15a C) 12a3 - 3a5 + 5 D) 4a2 - 3a4 + 5
75)
Objective: (5.6) Divide Polynomial by Monomial
Divide using long division.
76) (x2 + 7x - 18) ÷ ( x + 9)
A) x2 - 2 B) x - 2 C) x2 + 8x - 9 D) x + 2
76)
Objective: (5.6) Divide Using Long Division (No Remainder)
Factor out the GCF using the Distributive Property.
77) 3x2y6 + 15x2y5
A) 3x5y2(y + 5) B) y + 5 C) 3x2y5(y + 5) D) x2y5(3y + 5)
77)
Objective: (6.1) Factor Out GCF
78) 5x(3x + 4) - 4(3x + 4)
A) (5x - 4)(3x + 4) B) (15x + 4)(x - 4) C) (15x - 4)(x + 4) D) (5x + 4)(3x - 4)
78)
Objective: (6.1) Factor Out GCF (Binomial Factor)
Factor by grouping.
79) x2 + 5x + xy + 5y
A) (x - 5)(x + y) B) (x + 5)(x + y) C) (x + 5)(x - y) D) (x - 5)(x - y)
79)
Objective: (6.1) Factor by Grouping
15
80) yx - 9x - 5y + 45
A) (y - 9)(x - 5) B) (y + 9)(x + 5) C) (y + 9)(x - 5) D) (y - 9)(x + 5)
80)
Objective: (6.1) Factor by Grouping
Factor, if possible, using the difference or sum of squares. If a polynomial is not factorable, write ʺprime.ʺ
81) 16k2 - 81m2
A) (4k + 9m)2 B) prime
C) (4k - 9m)2 D) (4k + 9m)(4k - 9m)
81)
Objective: (6.2) Factor Sum or Difference of Squares
Factor using the sum or difference of cubes.
82) x3 - 512y3
A) (x + 8y)(x2 - 8xy + 64y2) B) (x - 8y)(x2 + 8xy + 64y2)
C) (x + 512y)(x2 + y2) D) (x - 8y)(x2 + 64y2)
82)
Objective: (6.2) Factor Sum or Difference of Cubes
Using the general factoring strategy, factor completely. If a polynomial is not factorable, write ʺprime.ʺ
83) 4x2 - 196
A) 4(x - 7)2 B) (4x + 28)(x - 7) C) 4(x + 7)(x - 7) D) (4x + 7)(x - 28)
83)
Objective: (6.2) Factor Using General Strategy
84)25
121m2 -
9
4
A)5
11m +
3
2
2B)
5
11m +
3
2 5
11m -
3
2
C)5
11m -
3
2
2D) prime
84)
Objective: (6.2) Solve Challenge Problem
Factor the trinomial using the AC Method. If a trinomial is not factorable, write ʺprime.ʺ
85) 4x2 + 12x + 9
A) (4x + 3)(x + 3) B) (2x - 3)(2x - 3) C) prime D) (2x + 3)(2x + 3)
85)
Objective: (6.3) Factor Using AC Method
86) 15x2 - 14x - 8
A) (3x - 4)(5x + 2) B) (x - 4)(15x + 2) C) (3x + 4)(5x - 2) D) (5x - 4)(3x + 2)
86)
Objective: (6.3) Factor Using AC Method
Factor the trinomial using the Educated Guess-and-Test Method. If a trinomial is not factorable, write ʺprime.ʺ
87) 15x2 + 16xy + 4y2
A) (3x + 2y)(5x + 2y) B) (3x - 2y)(5x - 2y)
C) (15x + y)(x + 4y) D) (15x + 2y)(x + 2y)
87)
Objective: (6.3) Factor Using Educated Guess-and-Test Method
16
Factor the trinomial using the Modified Guess-and-Test Method. If the trinomial is not factorable, write ʺprime.ʺ
88) x2 - x - 30
A) prime B) (x + 5)(x - 6) C) (x + 1)(x - 30) D) (x + 6)(x - 5)
88)
Objective: (6.4) Factor Using Modified Guess-and-Test Method
89) x2 + 7x - 44
A) (x + 11)(x - 4) B) (x - 11)(x + 4) C) prime D) (x - 11)(x + 1)
89)
Objective: (6.4) Factor Using Modified Guess-and-Test Method
90) u2 - 2uv - 48v2
A) (u - 6v)(u + v) B) (u + 6v)(u - 8v) C) (u - 6v)(u + 8v) D) (u - v)(u + 8v)
90)
Objective: (6.4) Factor Using Modified Guess-and-Test Method
Determine if the trinomial is a perfect square trinomial. If it is, factor it. If it is not, write ʺprime.ʺ
91) x2 + 16x + 64
A) (x + 8)2 B) (x + 8)(x - 8) C) (x - 8)2 D) prime
91)
Objective: (6.4) Factor Perfect Square Trinomial
92) b2 - 36b + 324
A) (b + 18)(b - 18) B) (b - 18)2 C) prime D) (b + 18)2
92)
Objective: (6.4) Factor Perfect Square Trinomial
93) 64x2 - 48xy + 9y2
A) prime B) (8x - y)2 C) (8x - 3y)2 D) (8x + 3y)2
93)
Objective: (6.4) Factor Perfect Square Trinomial
Factor the trinomial using the general factoring strategy. If a trinomial is not factorable, write ʺprime.ʺ
94) 5x2 - 5x - 30
A) (5x + 10)(x - 3) B) prime C) 5(x - 2)(x + 3) D) 5(x + 2)(x - 3)
94)
Objective: (6.4) Factor Using General Strategy
95) y3 + 12y2 + 36y
A) (y2 + 36)(y + 1) B) y(y + 6)(y - 6) C) y(y + 36)(y + 1) D) y(y + 6)2
95)
Objective: (6.4) Factor Using General Strategy
Factor the polynomial completely using the general factoring strategy. If the polynomial is not factorable, write ʺprime.ʺ
96) 3(x - 2) - a(x - 2)
A) (3x + 2)(x - a) B) (3 - a)(x - 2) C) 3a(x - 2) D) (3x - 2)(x - a)
96)
Objective: (6.5) Factor Out Common Factor
Solve the equation using the Zero Factor Property and state the solution set.
97) (9y + 20)(2y + 25) = 0
A) - 20
9, -
25
2B) -
9
11, -
2
25C) {11, 23} D)
20
9, 25
2
97)
Objective: (6.6) Solve Equation Using Zero Factor Property (Equation = 0)
17
98) 56n2 + 16n = 0
A) - 2
7, 0 B) -
2
7, 16 C) -
2
7D) {0}
98)
Objective: (6.6) Solve Equation Using Zero Factor Property (Equation = 0)
99) x2 - x = 20
A) {-4, -5} B) {4, 5} C) {1, 20} D) {-4, 5}
99)
Objective: (6.6) Solve Equation Using Zero Factor Property (Equation ≠ 0)
100) x(x - 3) = 54
A) {6, -9} B) {-6, -9} C) {-6, 9} D) {6, 9}
100)
Objective: (6.6) Solve Equation Using Zero Factor Property (Equation ≠ 0)
Simplify the rational expression.
101)3x - 15
x2 - 25
A) - 3
x + 5B)
3
x - 5C) -
12
x - 25D)
3
x + 5
101)
Objective: (7.1) Simplify Rational Expression
102)y2 - 2y - 8
y2 + 8y + 12
A)y - 4
y + 6B) -
y2 - 2y - 8
y2 + 8y + 12C)
-2y + 8
8y - 8D)
-2y - 8
8y + 12
102)
Objective: (7.1) Simplify Rational Expression
Multiply the rational expressions and write the answer in lowest terms.
103)8y4x
30 ·
10
32x3y2
A)y2
12x2B)
x2y2
12C)
1
12x2y2D)
12y2
x2
103)
Objective: (7.2) Multiply Rational Expressions
104)6y4x
27 ·
9
24x3y2
A)1
12x2y2B)
12y2
x2C)
x2y2
12D)
y2
12x2
104)
Objective: (7.2) Multiply Rational Expressions
105)a2 - 9b2
25ab2 ·
5a2b
a - 3b
A)a2 + 3ab
5B)
a2 + 3ab
5bC)
a + 3b
5abD)
a2 - 3ab
5b
105)
Objective: (7.2) Multiply Rational Expressions
18
Divide the rational expressions and write the answer in lowest terms.
106)m2 - 4
m2 + 4m - 12 ÷
m2 - 4m - 12
m - 2
A)m + 2
(m + 6)(m - 6)B)
m - 2
(m + 6)(m - 6)C)
m - 2
m - 6D)
m - 2
m2
106)
Objective: (7.2) Divide Rational Expressions
Add or subtract the rational expressions with common denominators. Write the answer in lowest terms.
107)7x + 10
2 -
5x
2
A) x + 10 B) 2x + 5 C) x + 5 D) 5x
107)
Objective: (7.3) Add or Subtract with Common Denominator
Perform the indicated operations and write the answer in lowest terms.
108)4
x +
7
x - 3
A)11x - 12
x(x - 3)B)
11x - 12
x(3 - x)C)
12x - 11
x(3 - x)D)
12x - 11
x(x - 3)
108)
Objective: (7.3) Add or Subtract with Unlike Denominators I
109)4
x + 5 -
6
x - 5
A)-2x + 50
(x + 5)(x - 5)B)
-2
(x + 5)(x - 5)C)
-2x + 10
(x + 5)(x - 5)D)
-2x - 50
(x + 5)(x - 5)
109)
Objective: (7.3) Add or Subtract with Unlike Denominators I
110)5w
w + 9 +
5
w
A)5w2 + 5w + 5
w(w + 9)B)
5w2 + 5
w(w + 9)
C)5w2 + 5w + 45
w(w + 9)D)
5w + 5
w(w + 9)
110)
Objective: (7.3) Add or Subtract with Unlike Denominators I
111)16
x2 - 64 +
1
x + 8
A)1
x + 8B)
17
x2 - 64C)
1
8 - xD)
1
x - 8
111)
Objective: (7.3) Add or Subtract with Unlike Denominators I
19
Simplify the complex fraction.
112)
14
y2 - 49
35
y - 7
A)5
2(y + 7)B)
2
5(y + 7)C)
2
5(y - 7)D)
2(y + 7)
5
112)
Objective: (7.4) Simplify Complex Fractions by Multiplying by Reciprocal
113)
64 - 8
z
8 - 1
z
A) 8 B) 8z C)1
8D)
8
z
113)
Objective: (7.4) Simplify Complex Fractions by Multiplying by Reciprocal
114)
3
x +
2
x2
9
x2 -
4
x
A)1
3 - 2xB)
1
3x - 2C)
3x2 + 2
9 - 4xD)
3x + 2
9 - 4x
114)
Objective: (7.4) Simplify Complex Fractions by Multiplying by LCD/LCD
115)
5
x -
4
y
2
x+ 3
y
A)5x - 4y
2x + 3yB)
5y + 4x
2y - 3xC)
5y - 4x
2y + 3xD)
x + y
5(x - y)
115)
Objective: (7.4) Simplify Complex Fractions by Multiplying by LCD/LCD
116)
x
36 -
1
x
1 + 6
x
A)36
x - 6B)
x + 6
36C)
x - 6
36D)
36
x + 6
116)
Objective: (7.4) Simplify Complex Fractions by Multiplying by LCD/LCD
20
117)
9 + 3
x
x
4 +
1
12
A) 1 B)x
36C)
36
xD) 36
117)
Objective: (7.4) Simplify Complex Fractions by Multiplying by LCD/LCD
118)
36t2 - 16u2
t u
6
u -
4
t
A) 6t + 4u B) 4t + 6u C)tu
6t + 4uD)
4t + 6u
tu
118)
Objective: (7.4) Simplify Complex Fractions by Multiplying by LCD/LCD
Find any excluded values and state the domain of the rational function using interval notation or set -builder notation as
appropriate.
119) f(x) = 8 + 6
x + 4
A) D = (-∞, ∞) B) D = {x|x ≠ -4 and x ≠ 4}
C) D = {x|x ≠ -4} D) D = {x|x ≠ -6}
119)
Objective: (7.5) State Domain of Rational Function
120) f(y) = y2 - 24y
6y
A) D = {y| y ≠ 6} B) D = y|y ≠ 1
6
C) D = {y|y ≠ 0} D) D = {y|y ≠ 0 and y ≠ 24}
120)
Objective: (7.5) State Domain of Rational Function
121) f(x) = x2 - 36
x2 - 11x + 30
A) D = {x|x ≠ -5 and x ≠ -6} B) D = {x|x ≠ 6 and x ≠ -6}
C) D = {x|x ≠ 0} D) D = {x|x ≠ 5 and x ≠ 6}
121)
Objective: (7.5) State Domain of Rational Function
Solve the equation.
122)6
x -
1
4 =
4
x
A) {-8} B) {-2} C) {8} D)2
3
122)
Objective: (7.5) Solve Equation Involving Rational Expression
21
123)2
y + 2 -
5
y - 2 =
10
y2 - 4
A) {8} B) { 4} C) {-8} D) {24}
123)
Objective: (7.5) Solve Equation Involving Rational Expression
Solve the formula for the indicated variable.
124) L = P
2 - W for P
A) P = 2L + 2W B) P = 2LW C) P = 2L + W D) P = 2L - 2W
124)
Objective: (7.5) Solve Formula for Indicated Variable
125)1
a +
1
b = c for a
A) a = 1
c - b B) a =
b
bc - 1C) a =
1
bcD) a = bc -
1
b
125)
Objective: (7.5) Solve Formula for Indicated Variable
Translate the statement and find the variation constant, k.
126) y varies directly with x and y = 15 when x = 12.
A)4
5B) 3 C)
1
3D)
5
4
126)
Objective: (7.6) Find Variation Constant
Solve the variation problem.
127) C varies directly with v. If C = 225 when v = 9, find C if v = 14.
A) 126 B) 336 C) 350 D) 375
127)
Objective: (7.6) Solve Direct, Indirect, or Joint Variation Problems
Simplify using the product rule for radicals.
128) 180
A) 5 6 B) 30 C) 6 5 D) 13
128)
Objective: (8.1) Simplify Using Product Rule
Write in simplified radical form. Assume that all variables represent positive real numbers.
129) 169x6yz9
A) 13x4z7 y B) 6.5x3z4 xyz C) 6.5x3yz4 D) 13x3z4 yz
129)
Objective: (8.1) Write in Simplified Radical Form
Perform the indicated operations. Write the answer in simplified radical form. Assume that all variables represent
positive real numbers.
130) 12 2 - 8 2 - 2
A) -5 2 B) 3 2 C) 4 2 D) 5 2
130)
Objective: (8.1) Add/Subtract Square Roots
22
Using the Pythagorean Theorem, a2 + b2 = c2, find the missing length of the side of the triangle. Write your answer in
simplified radical form.
131)
8
9
A) 145 B) 145 C) 17 D) 17
131)
Objective: (8.1) Solve Application
Multiply. Write the answer in simplified radical form. Assume that all variables represent positive real numbers.
132) (1 + 3 7)(1 - 3 7)
A) -62 B) 1 + 6 7 C) 1 - 6 7 D) 64
132)
Objective: (8.2) Multiply Square Roots (Distribute/FOIL/Special Product)
Solve the problem by utilizing the 4Pʹs: Prepare, Plan, Process, and Ponder. Find the speed, S, of the accident vehicle
using the formula S = sD
d, where s is the speed of the test vehicle, D is the length of the skid marks at the accident
scene, and d is the length of the skid marks left by the test vehicle.
133) Skid marks at an accident scene are 125 feet in length. If the speed of the test vehicle was 36 mph
and it left 48 feet of skid marks, how fast was the other car traveling before the accident?
A) 5 10 mph B) 5 15 mph C) 15 10 mph D) 15 15 mph
133)
Objective: (8.2) Solve 4Ps Application
Solve and write the solution using set notation.
134) 7 - x = x - 1
A) { } B) {-2, 3} C) {-2} D) {3}
134)
Objective: (8.3) Solve Equation Containing Square Root (Square Binomial)
Solve the problem by utilizing the 4Pʹs: Prepare, Plan, Process, and Ponder. The formula t = 2πL
g represents the time
(in seconds) for a pendulum of length L (in feet) to complete one cycle, where g is the gravitational constant of
approximately 32 feet per second squared. Use the formula to find the exact and approximate lengths in the following
application.
135) Find the length of the pendulum in a clock tower if it takes 5 seconds for the pendulum to
complete one cycle.
A) L = 200
π ft., or approximately 63.65 ft. B) L =
100
π2 ft., or approximately 10.13 ft.
C) L = 200
π2 ft., or approximately 20.26 ft. D) L =
40
π2 ft., or approximately 4.05 ft.
135)
Objective: (8.3) Solve 4Ps Application
23
Solve the problem by utilizing the 4Pʹs: Prepare, Plan, Process, and Ponder.
136) The radius of a sphere is given by the formula r = S
4π, where S is the surface area of the sphere.
Use the formula to solve the application. Joan Lone is an astronomy student at a local community
college. As part of her final project she has designed a model of the solar system. In this model, the
sphere representing the planet Jupiter has a surface area of approximately 180 square centimeters.
Find the radius of this sphere. Give your answer in exact form and as a decimal rounded to the
nearest tenth of a centimeter.
A)6 5π
π cm or 7.6 cm B)
3 5π
π cm or 3.8 cm
C)3 5
π cm or 2.1 cm D)
18 5π
π cm or 22.7 cm
136)
Objective: (8.4) Solve 4Ps Application
Simplify using the product rule or quotient rule for radicals. Write the answer in simplified radical form. Assume that
all variables represent positive real numbers.
137)3
-27a11b13
A) -3ab3a5b4 B) 3 a13b11 C) -3a3b4
3a2b D) -3a2b
3a3b4
137)
Objective: (8.5) Simplify Radical Using Product Rule or Quotient Rule
Solve and write the solution using set notation.
138)42x - 4 + 3 = 7
A) {260} B) {10} C) {130} D) {-38}
138)
Objective: (8.6) Solve Equation Containing Higher Root
Find the functional value and write the answer as an ordered pair.
139) h(x) = 3x2 - 7x - 4, h(-5)
A) (-5, -114) B) (-5, -44) C) (-5, 36) D) (-5, 106)
139)
Objective: (9.1) Find Functional Value (Number)
140) g(t) = 8t2 - 5t, g1
2
A)1
2, 1
2B)
1
2, -
1
2C)
1
2, 3
2D)
1
2, -
3
2
140)
Objective: (9.1) Find Functional Value (Number)
141) f(x) = 5x - 4 , f(-3)
A) (-3, 11) B) (-3, -19) C) (-3, -11) D) (-3, 19)
141)
Objective: (9.1) Find Functional Value (Number)
24
Find the following function and its domain.
142) Let f(x) = 4 - 9x and g(x) = -2x + 9. Find (f + g)(x).
A) -7x + 13, D = x x ≠ - 13
7B) -2x + 4, D = x x ≠ 2
C) 2x, D = (-∞, ∞) D) -11x + 13, D = (-∞, ∞)
142)
Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions
143) Let f(x) = 2x2 - 3 and g(x) = 7x - 4. Find (f - g)(x).
A) 2x2 - 7x + 1, D = (-∞, ∞) B) -5x - 7, D = x x ≠ - 7
5
C) 2x2 - 7x - 7, D = (-∞, ∞) D) 9x + 1, D = {x x ≠ 1}
143)
Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions
144) Let f(x) = 5x + 1 and g(x) = 2x - 5. Find f
g(x).
A)2x - 5
5x + 1, D = x x ≠ -
1
5B)
5x + 1
2x - 5, D = x x ≠
5
2
C)2x - 5
5x + 1, D = x x ≠
5
2D)
5x + 1
2x - 5, D = x x ≠ -
1
5
144)
Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions
145) Let f(x) = 5x2 - 2 and g(x) = 4x + 1. Find (f · g)(x).
A) 20x3 + 5x2 - 8x - 2, D = (-∞, ∞) B) 5x2 + 4x - 2, D = (-∞, ∞)
C) 20x3 - 8x - 2, D = {x x ≠ 0} D) 20x3 + 5x2 - 2, D = (-∞, ∞)
145)
Objective: (9.2) Find Sum, Difference, Product, or Quotient of Functions
Graph the function by plotting points. State the domain and range.
146) f(x) = 5
x-5 5
y
5
-5
x-5 5
y
5
-5
146)
25
A) D = {5}
R = (-∞, ∞)
x-5 5
y
5
-5
x-5 5
y
5
-5
B) D = (-∞, ∞)
R = {5}
x-5 5
y
5
-5
x-5 5
y
5
-5
C) D = {5}
R = (-∞, ∞)
x-5 5
y
5
-5
x-5 5
y
5
-5
D) D = (-∞, ∞)
R = (-∞, ∞)
x-5 5
y
5
-5
x-5 5
y
5
-5
Objective: (9.3) Graph Function
147) g(x) = x - 1
x
y
x
y
147)
26
A) D = [0, ∞)
R = [1, ∞)
x-16 -12 -8 -4 4 8 12 16
y
12
8
4
-4
-8
-12
x-16 -12 -8 -4 4 8 12 16
y
12
8
4
-4
-8
-12
B) D = [-1, ∞)
R = [0, ∞)
x-16 -12 -8 -4 4 8 12 16
y
12
8
4
-4
-8
-12
x-16 -12 -8 -4 4 8 12 16
y
12
8
4
-4
-8
-12
C) D = [0, ∞)
R = [-1, ∞)
x-16 -12 -8 -4 4 8 12 16
y
12
8
4
-4
-8
-12
x-16 -12 -8 -4 4 8 12 16
y
12
8
4
-4
-8
-12
D) D = [1, ∞)
R = [0, ∞)
x-16 -12 -8 -4 4 8 12 16
y
12
8
4
-4
-8
-12
x-16 -12 -8 -4 4 8 12 16
y
12
8
4
-4
-8
-12
Objective: (9.3) Graph Function
148) f(x) = 5 - x
x
y
x
y
148)
27
A) D = (-∞, 5]
R = (-∞, 0]
x-5 5
y
5
-5
x-5 5
y
5
-5
B) D = [5, ∞)
R = [0, ∞)
x-10 10
y
5
-5
x-10 10
y
5
-5
C) D = [0, ∞)
R = [-5, ∞)
x-5 5
y
5
-5
x-5 5
y
5
-5
D) D = (-∞, 5]
R = [0, ∞)
x-5 5
y
5
-5
x-5 5
y
5
-5
Objective: (9.3) Graph Function
28
Match the function with the appropriate graph of the transformation of the function g(x) = x2.
149) f(x) = (x - 3)2
A)
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
B)
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
C)
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
D)
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
149)
Objective: (9.4) Match Function to Its Graph
29
150) f(x) = -x2 + 2
A)
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
B)
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
C)
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
D)
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
150)
Objective: (9.4) Match Function to Its Graph
30
151) f(x) = (x + 4)2 - 5
A)
x-10 -8 -6 -4 -2 2 4 6 8
y10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8
y10
8
6
4
2
-2
-4
-6
-8
-10
B)
x-10 -8 -6 -4 -2 2 4 6 8
y10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8
y10
8
6
4
2
-2
-4
-6
-8
-10
C)
x-10 -8 -6 -4 -2 2 4 6 8
y10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8
y10
8
6
4
2
-2
-4
-6
-8
-10
D)
x-10 -8 -6 -4 -2 2 4 6 8
y10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8
y10
8
6
4
2
-2
-4
-6
-8
-10
151)
Objective: (9.4) Match Function to Its Graph
Using transformations and/or reflections and one of the basic graphs, state the transformation and/or reflection and
sketch the function.
152) g(x) = (x - 3)2
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
152)
31
A) This is the graph of f(x) = x2 shifted
to the left 3 units.
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
B) This is the graph of f(x) = x2 shifted
to the right 3 units.
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
C) This is the graph of f(x) = x2 shifted
up 3 units.
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
D) This is the graph of f(x) = x2 shifted
down 3 units.
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
Objective: (9.4) Use Transformations to Graph Function
153) f(x) = x + 3
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
153)
32
A) This is the graph of f(x) = x shifted
to the left 3 units.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
B) This is the graph of f(x) = x shifted
up 3 units.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
C) This is the graph of f(x) = x shifted
down 3 units.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
D) This is the graph of f(x) = x shifted
to the right 3 units.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Objective: (9.4) Use Transformations to Graph Function
154) g(x) = (x + 3)2 - 1
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
154)
33
A) This is the graph of f(x) = x2 shifted
to the right 3 units and then shifted
down 1 unit.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
B) This is the graph of f(x) = x2 shifted
to the left 1 unit and then shifted
up 3 units.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
C) This is the graph of f(x) = x2 shifted
to the right 1 unit and then shifted
up 3 units.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
D) This is the graph of f(x) = x2 shifted
to the left 3 units and then shifted
down 1 unit.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Objective: (9.4) Use Transformations to Graph Function
155) f(x) = x + 2 - 7
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
155)
34
A) This is the graph of f(x) = x shifted
7 units to the left and then shifted
up 2 units.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
B) This is the graph of f(x) = x shifted
7 units to the right and then shifted
up 2 units.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
C) This is the graph of f(x) = x shifted
to the right 2 units and then shifted
down 7 units.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
D) This is the graph of f(x) = x shifted
to the left 2 units and then shifted
down 7 units.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Objective: (9.4) Use Transformations to Graph Function
156) f(x) = - x - 6
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
156)
35
A) This is the graph of f(x) = x shifted
right 6 units and then reflected about
the x-axis.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
B) This is the graph of f(x) = x shifted
left 6 units and then reflected about
the y-axis.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
C) This is the graph of f(x) = x shifted
left 6 units and then reflected about
the x-axis.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
D) This is the graph of f(x) = x shifted
right 6 units and then reflected about
the y-axis.
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Objective: (9.4) Use Transformations and Reflections to Graph Function
157) h(x) = - x + 3 - 5
x-20 -16 -12 -8 -4 4 8 12 16 20
y
20
16
12
8
4
-4
-8
-12
-16
-20
x-20 -16 -12 -8 -4 4 8 12 16 20
y
20
16
12
8
4
-4
-8
-12
-16
-20
157)
36
A) This is the graph of f(x) = x shifted
to the right 3 units, reflected about the
x-axis and then shifted down 5 units.
x-20 -16-12 -8 -4 4 8 12 16 20
y
20
16
12
8
4
-4
-8
-12
-16
-20
x-20 -16-12 -8 -4 4 8 12 16 20
y
20
16
12
8
4
-4
-8
-12
-16
-20
B) This is the graph of f(x) = x shifted
to the left 3 units, reflected about the
x-axis and then shifted down 5 units.
x-20 -16-12 -8 -4 4 8 12 16 20
y
20
16
12
8
4
-4
-8
-12
-16
-20
x-20 -16 -12 -8 -4 4 8 12 16 20
y
20
16
12
8
4
-4
-8
-12
-16
-20
C) This is the graph of f(x) = x shifted
to the right 3 units, reflected about the
y-axis and then shifted down 5 units.
x-20 -16-12 -8 -4 4 8 12 16 20
y
20
16
12
8
4
-4
-8
-12
-16
-20
x-20 -16-12 -8 -4 4 8 12 16 20
y
20
16
12
8
4
-4
-8
-12
-16
-20
D) This is the graph of f(x) = x shifted
to the left 3 units, reflected about the
y-axis and then shifted down 5 units.
x-20 -16-12 -8 -4 4 8 12 16 20
y
20
16
12
8
4
-4
-8
-12
-16
-20
x-20 -16 -12 -8 -4 4 8 12 16 20
y
20
16
12
8
4
-4
-8
-12
-16
-20
Objective: (9.4) Use Transformations and Reflections to Graph Function
Perform the indicated operations and write the answer in the standard form a + bi.
158)7i
2 - 14i
A) - 49
100 +
7
100i B)
7
100 +
49
100 i C)
49
100 +
7
100i D)
7
100 -
49
100 i
158)
Objective: (10.1) Multiply or Divide Complex Numbers
159)5 - i
-9 + 4i
A)49
97 -
11
97 i B)
1
97 -
11
97 i C) -
11
97 i D) -
49
97 -
11
97 i
159)
Objective: (10.1) Multiply or Divide Complex Numbers
37
Solve using the Zero Factor Property.
160) 7x2 + 19x - 6 = 0
A) - 1
3, 7
2B) -
7
2, 1
3C) -
2
7, 3 D) -3,
2
7
160)
Objective: (10.2) Solve Using Zero Factor Property
161) 4x2 + 7x - 15 = 0
A) - 5
4, 3 B) -
4
5, 1
3C) -3,
5
4D) -
1
3, 4
5
161)
Objective: (10.2) Solve Using Zero Factor Property
162) 8x2 + 17x - 21 = 0
A) -3, 7
8B) -
1
3, 8
7C) -
7
8, 3 D) -
8
7, 1
3
162)
Objective: (10.2) Solve Using Zero Factor Property
Solve using the Square Root Property.
163) x2 = 25
A) {5} B) {-5, 5} C) {625} D) - 1
5, 1
5
163)
Objective: (10.2) Solve Using Square Root Property
164) x2 = 18
A) {-9 2, 9 2} B) {-3 2, 3 2} C) {3 2} D) {9 2}
164)
Objective: (10.2) Solve Using Square Root Property
165) (x - 7)2 = 25
A) {32} B) {5, -5} C) {12, 2} D) {2, -12}
165)
Objective: (10.2) Solve Using Square Root Property
166) (4x + 3)2 - 7 = 0
A)3 - 7
4, 3 + 7
4B)
-3 - 7
4,
-3 + 7
4
C) - 5
2 , 1 D)
7 - 3
4,
7 + 3
4
166)
Objective: (10.2) Solve Using Square Root Property
Solve by completing the square.
167) x2 - 6x + 18 = 0
A) {0, 6} B) {3 - 3i, 3 + 3i} C) {3 - 9i, 3 + 9i} D) {3 + 3i}
167)
Objective: (10.2) Solve by Completing the Square
168) 3x2 + 15x = - 18
A) {-3, 2} B) {-3, -2} C) - 1
2, 1
2D) {2, 3}
168)
Objective: (10.2) Solve by Completing the Square
38
Solve using the Quadratic Formula.
169) 5x2 + 8x = 4
A)5
2, 2 B) 0,
8
5C) -
8
5, 0 D) -2,
2
5
169)
Objective: (10.3) Solve Using Quadratic Formula
Solve by the method of your choice.
170) x2 + 2x - 24 = 0
A) {- 6, 4} B) {6, -4} C) {-24, 0} D) {6, 4}
170)
Objective: (10.3) Solve Quadratic Equation by Any Method
171) x2 + 14x + 74 = 0
A) {-7 - 5i, -7 + 5i} B) {-7 + 5i}
C) {-7 - 25i, -7 + 25i} D) {-12, -2}
171)
Objective: (10.3) Solve Quadratic Equation by Any Method
Solve the application using the Pythagorean theorem.
172) A bird flies 36 meters in a straight line from the top of a vertical cliff to a point on the ground 23
meters from the base of the cliff. Find the height of the cliff. Round to the nearest hundredth of a
meter.
36 m
23 m
A) Approximately 42.72 meters B) Approximately 27.15 meters
C) Approximately 13 meters D) Approximately 27.69 meters
172)
Objective: (10.3) Solve Application
173) One end of a guy wire is attached to the top of a 13-foot pole and the other end is anchored into
the ground 9 feet from the base of the pole. Find the length of the guy wire. Round to the nearest
tenth of a foot.
13 feet
9 feet
A) Approximately 15.8 feet B) Approximately 22.5 feet
C) Approximately 22 feet D) Approximately 15.3 feet
173)
Objective: (10.3) Solve Application
39
Solve the formula for the indicated variable.
174) V = 1
3s2h for s (volume of a square pyramid)
A) s = 3Vh B) s = 3Vh
hC) s =
3Vh
3hD) s =
3V
h
174)
Objective: (10.4) Solve Application
Determine a) if the parabola opens up/down or left/right, b) the axis of symmetry, c) the vertex, and d) the intercepts.
Then graph the parabola given by the quadratic equation.
175) y = x2 - 9
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
A) a. up, b. x = 0, c. (0, -9), d. (-3, 0) and (3, 0)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
B) a. down, b. x = 0, c. (0, -9), d. none
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
175)
40
C) a. up, b. x = 0, c. (0, 9), d. none
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
D) a. up, b. x = -9, c. (-9, 0), d. (-9, 0)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
Objective: (11.1) Graph Parabola and State Characteristics
Graph the quadratic equation.
176) y = (x - 3)2 + 6
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
176)
41
A)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
B)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
C)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
D)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
Objective: (11.1) Graph Parabola
177) y = (x + 4)2 + 5
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
177)
42
A)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
B)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
C)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
D)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
Objective: (11.1) Graph Parabola
178) y = (x - 3)2
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
178)
43
A)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
B)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
C)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
D)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
Objective: (11.1) Graph Parabola
179) y = 3(x - 4)2 + 6
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
179)
44
A)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
B)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
C)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
D)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
Objective: (11.1) Graph Parabola
180) y = 3(x - 1)2 - 5
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
180)
45
A)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
B)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
C)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
D)
x-10 -5 5 10
y
10
5
-5
-10
x-10 -5 5 10
y
10
5
-5
-10
Objective: (11.1) Graph Parabola
Solve the application.
181) An arrow is fired into the air with an initial velocity of 64 feet per second. The height in feet of the
arrow t seconds after it was shot into the air is given by the function h(t) = -16t2 + 64t. Find the
maximum height of the arrow.
A) 64 feet B) 96 feet C) 32 feet D) 192 feet
181)
Objective: (11.1) Solve Application
182) A person is standing on the top of a building 50 feet above the ground. They project an object
upward with an initial velocity of 40 feet per second. The objectʹs distance above the ground, d,
after t seconds may be found by the formula d = -16t2 + 40t + 50. What is the maximum height the
object will reach and how much time does it take to reach that height?
A) maximum height = 75 ft; time = 1.25 seconds
B) maximum height = 50 ft; time = 2.5 seconds
C) maximum height = 75 ft; time = 2.5 seconds
D) maximum height = 50 ft; time = 1.25 seconds
182)
Objective: (11.1) Solve Application
46
Answer KeyTestname: AT9210ACCUPLACER2B
1) B
2) C
3) A
4) C
5) D
6) C
7) B
8) A
9) D
10) B
11) B
12) C
13) C
14) C
15) A
16) D
17) A
18) B
19) A
20) D
21) B
22) D
23) A
24) D
25) D
26) B
27) B
28) A
29) C
30) B
31) D
32) A
33) A
34) A
35) B
36) C
37) C
38) A
39) C
40) C
41) B
42) C
43) D
44) B
45) B
46) C
47) A
48) C
49) D
50) D
47
Answer KeyTestname: AT9210ACCUPLACER2B
51) B
52) D
53) C
54) B
55) D
56) D
57) C
58) C
59) A
60) B
61) B
62) D
63) D
64) B
65) A
66) C
67) A
68) A
69) B
70) B
71) D
72) D
73) A
74) C
75) D
76) B
77) C
78) A
79) B
80) A
81) D
82) B
83) C
84) B
85) D
86) A
87) A
88) B
89) A
90) B
91) A
92) B
93) C
94) D
95) D
96) B
97) A
98) A
99) D
100) C
48
Answer KeyTestname: AT9210ACCUPLACER2B
101) D
102) A
103) A
104) D
105) B
106) B
107) C
108) A
109) D
110) C
111) D
112) B
113) A
114) D
115) C
116) C
117) C
118) A
119) C
120) C
121) D
122) C
123) C
124) A
125) B
126) D
127) C
128) C
129) D
130) B
131) B
132) A
133) D
134) D
135) C
136) B
137) C
138) C
139) D
140) B
141) D
142) D
143) A
144) B
145) A
146) B
147) D
148) D
149) A
150) C
49
Answer KeyTestname: AT9210ACCUPLACER2B
151) B
152) B
153) A
154) D
155) D
156) A
157) B
158) A
159) D
160) D
161) C
162) A
163) B
164) B
165) C
166) B
167) B
168) B
169) D
170) A
171) A
172) D
173) A
174) B
175) A
176) C
177) B
178) C
179) A
180) C
181) A
182) A
50